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14. Second and higher order ODEs
- Class notes • 4 pages • 2019
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Looking at steady state solution for modelling the populations of predators and prey with graphs. Constructing systems of equations for different stages of life to model the population of a species.
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13. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Reduction of order method to find all terms of the homogeneous solution. Euler Cauchy Equations and the types of solution for the roots of the characteristic equation. Example using Reduction of order finding the general solution. Modelling Mathematical ecology, by looking at a fish example, finding solutions to a system of equations of how different factors affect fish populations.
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Advance Math
- Class notes • 1 pages • 2020
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This is for electrical engineering student related subjects for you references in your subjects. Please analyze carefully the solutions. Email me at if you have questions. Thank you
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5. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Example of a separable solution. Existence and Uniqueness Theorem (no proof) with two example questions. Showing how to work out the integrating factor to make exact ODEs exact.
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33. More partial differential equations
- Class notes • 6 pages • 2019
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Looking at the wave equation and solving using polar coordinates for a wave propagating on the surface of a circular pool. Special case with no angular dependence and finding solutions.
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21. Representing periodic functions by Fourier series & PDEs and waves
- Class notes • 4 pages • 2019
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Graph and solve fourier series for square wave with arbitrary period. Fourier Cosine and Sine series with matlab example. Half-range expansion with examples.
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17. Partial differential equations
- Class notes • 5 pages • 2019
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Example of Near constant car density continued with interpretation. D'Alembert's solutions with an example of some cars being able to pass other cars. Heat equation and solving it with separation of variables coming to the full general solution.
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12. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Damped system and the different scenarios and their solutions. Solutions plotted in matlab and graphed. Looked at Resonance in forced oscillations and the particular solution for this equation. Graph the solution of types of solution for the particular solution for different constant values and interpreted the results. Looked at more general methods of solving ODEs: finding a solution that is a factor multiple of a known solution.
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8. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Picard's Iteration method with example and using matlab to solve. Classification of ODEs: order and linearity. Initial value problem theory: autonomy, deterministism, homogeneous linear ODEs and superposition with proof. Different cases of equation giving examples of the different types and features.
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Partial Differential Equations - Lecture 9 Notes
- Class notes • 6 pages • 2019
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The aim of this course unit is to enable a student to:
1.	Demonstrate an understanding of methods used to solve partial differential equations and their engineering areas of application,
2.	Apply mathematical skills from partial differentiation to solve problems that require partial differentiation methods,
3.	Appreciate the role of partial differentiation in solving problems that are related to science and engineering.

At the end of this course unit, the student should be able to:
1.	Apply par...
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